Parrish was born in Vroomanton, Canada West (now Ontario), the son of Samuel Parrish and Jane Cash, and was educated at Uxbridge. He began work in the grain trade with his father and then, in 1879, moved to Huntsville where he operated a grist and flour mill. In 1881, Parrish moved to Manitoba and operated as a grain dealer in Brandon and then, later, in Winnipeg. In 1885, he married Annie Ellen Card. He was a member of Brandon town council for two years. Parrish also served as president of the Winnipeg Grain Exchange. In 1909, he co-founded the Parrish & Heimbecker grain company. He was also the director of Fidelity Trust Co., Equitable Trust Co., Capital Loan Co. and Inland Mortgage Co. Parrish was an honorary captain and paymaster with the 90th Winnipeg Rifles, and was a Methodist in religion.
He was first elected to the Manitoba legislature in the 1914 provincial election, defeating Conservative Harry W. Whitlaw by 910 votes in the constituency of Winnipeg South "B". The Conservatives won this election, and Parrish sat with his party in opposition.
In 1915, the Conservative administration of Rodmond P. Roblin was forced to resign from office amid a corruption scandal. A new election was called, which the Liberals won in a landslide. Parrish was easily re-elected in his constituency, defeating Conservative Lendrum McMeans by 3,332 votes. He served as a backbench supporter of Tobias C. Norris's administration for the next five years.
Winnipeg's electoral boundaries were dramatically changed before the 1920 provincial election. The city became a single ten-member constituency, with members elected by a single transferable ballot. Parrish finished 17th on the first count with 945 votes, and was eliminated on the 28th count.
- Bryce, George (1906). Manitoba, its resources and people. pp. 393–94. Retrieved 2012-12-02.
- "MLA Biographies - Deceased". Legislative Assembly of Manitoba.
- "William Bruce Parrish, LL.D., May 30, 1996". University of Manitoba. Retrieved 2012-12-02.
- "William Linton Parrish (1860-1949)". Memorable Manitobans. Manitoba Historical Society. Retrieved 2012-12-02.
- "Legislature Scandal". TimeLinks. Manitoba Historical Society. Retrieved 2012-11-29.